Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains

Experiments and Results • (c) Mass-Spring • Coupling patterns Deep learning for Data-driven simulators • Deep learning can build simulators from observations by learning the underlying differential equations ẋ𝑥 = 𝑓𝑓(𝑥𝑥). • crucial for the design & control of circuit, vehicle & robot. • Existing methods: • Neural ODEs for general ODEs [1] • HNNs for conservative systems [2] • Dissipative SymODENs for controls and dissipations [3] • CHNNs and PNNs for constraints and degeneracy [4,5] Limitations • Narrowed scope: Focuses only on mechanical systems and address only limited aspects as above • Monolithic structure: Treats a system as a single entity, and embeds the interactions between sub-components in a neural network, hindering interpretability Key Contributions • Unified Modeling: • Handles diverse physics domains (mechanical, electrical, hydraulic, etc.) and their interactions (multiphysics). • Handles various aspects, including energy conservation, dissipation, external inputs, and degeneracy. • Interpretability: Explicitly learns and identifies coupling patterns and component-wise characteristics from data. • Robustness: Improves modeling accuracy and long-term prediction stability by separating the interactions from component-wise behavior.